If you are enrolled in Phase I, the dose of brentuximab vedotin you receive will depend on when you joined this study. The first group of participants will receive a lower dose level of brentuximab vedotin than the highest one that was tolerated in the Pilot Phase, and will also receive azacitidine. If intolerable side effects are seen, up to 2 more groups will be enrolled and will receive a lower dose of brentuximab vedotin than the group before it. If intolerable side effects are not seen, the next phase of the study will begin.